Symplectic Elimination

TL;DR

The paper introduces a symplectic elimination algorithm that reduces symplectic matrices to diagonal form and provides a new matrix decomposition similar to SR and QR decompositions.

Contribution

It develops a novel symplectic elimination algorithm and a related matrix decomposition, expanding the tools for symplectic matrix analysis.

Findings

Algorithm effectively reduces symplectic matrices to diagonal form

Provides a new matrix decomposition similar to SR and QR

Enables new approaches in symplectic matrix analysis

Abstract

We develop the symplectic elimnation algorithm. This algorithm using simple row operations reduce a symplectic matrix to a diagonal matrix. This algorithm gives rise to a decomposition of an arbitrary matrix into a product of a symplectic matrix and a reduced matrix. This decomposition is similar to the SR decomposition studied for a long time, which is analogous to the QR decomposition.